Physical reconstruction or synthesis of three-dimensional sound fields can be implemented with Near Field Compensated Higher Order Ambisonics. This paper investigates the use of a fifty-node Lebedev grid, which is derived from rotationally-invariant quadrature rules. Special attention is paid to spatial aliasing artifacts at the capture and reproduction steps. While comparing a fifty-node Lebedev grid with a Fliege and a t-design grid that both use almost the same number of nodes, it is shown that the Lebedev grid provides the best performance in terms of sound field capture and reproduction. Finally, a multiband multiorder decoder is presented. These decoders take advantage of the inherent nested subgrids when following the rotationally-invariant quadrature approach. The importance of orthonormality of the spherical harmonics was highlighted in a context of physical encoding or reconstruction of a sound field with the Ambisonics approach. Simulation results are provided for the case of a three-band decoder using the three grids contained in the Lebedev grid. It was found that a multifrequency sound field can be reproduced accurately in the sweet-spot by using a combination of low-order decoder for low frequency and higher-order decoder for higher frequency.
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